This paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. In the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). However,, two significant criteria for each schedule in stochastic models are: expectable m...

We reason that if there are nurnbers, they are abstract and therefore acausal. The question thus arises as to how we have knowledge of these objects. My thesis consists of three parts, each of which explores a response to this question. Charles Parsons has argued that we know about the numbers because we can apprehend (or "intuit") some abstract objects such as expression-types which form a mod...

One is not required to be a mechanical engineer to drive a car and, considering the advanced state of mechanical engineering, most people limit their interest in what lies “under the hood” to finding a competent mechanic. Users of evaluation, risk, and decision analysis tools that are based on classical decision theory should be aware that, as is demonstrated below, classical MCDA (multi-criter...

BACKGROUND National Strategic Plans (NSPs) for HIV have become foundational documents that frame responses to HIV. Both Global Fund and PEPFAR require coordination with NSPs as a component of their operations. Despite the role of NSPs in country planning, no rigorous assessment of NSP targets and performance outcomes exists. We performed a quantitative analysis of the quality of NSP indicators ...

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"Compulsory Education Mathematics Curriculum Standards (2022 Edition)" clearly states that attention should be paid to mathematics culture, but at present, textbooks and classrooms still do not attach importance culture is really integrated into classroom teaching. For further exploring how integrate mathematical teaching, the traditional teaching design of Letters Represent Numbers transformed...

In this paper, a new model for resonance frequency of clamped circular corrugated diaphragm has been presented. First, an analytical analyzes has been carried out to derive mathematic expressions for mechanical sensitivity of diaphragm with residual stress. Next by using Rayleigh's method we present mathematical model to calculate the resonance frequency of corrugated diaphragm and investigate ...

Statistical convergence for sequences of fuzzy real numbers has been studied by various authors. In this paper we study the concept of statistical summability (C, 1) for fuzzy real numbers which for real numbers was introduced by Moricz [18]. We also construct some interesting examples. AMS Mathematical Subject Classification: 40A30, 40E05, 94D05

Generalized estimating equation solvers in R only allow for a few pre-determined options for the link and variance functions. We provide a package, geeM, which is implemented entirely in R and allows for user specified link and variance functions. The sparse matrix representations provided in the Matrix package enable a fast implementation. To gain speed, we make use of analytic inverses of the...

This paper demonstrates that it is possible to relax the commitment to numeric degrees of belief while retaining the desirable features of the Bayesian approach for representing and changing states of belief. We first present an abstract representation of states of belief and an associated notion of conditionalization that subsume their Bayesian counterparts. Next, we provide some symbolic and ...